I looked into this recently and if you own a foreign company (aka CFC: Controlled Foreign Corporation) you have to report that to the IRS. And once the IRS knows, then presumably the USCIS will find out as well.

Right, you've to report it. But the question is if that's actually against the rules - it's not entirely clear to me. I'm personally lucky enough to now have a greencard so I don't have to worry about it anymore...